416 SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 



about one-tentb smaller when such temperature differences occur at 

 15° C. instead of 0° C. Even if we consider also the greater latent heat, 

 this still does not compensate for the differences in the intensities of 

 precipitation, and suffices not for an explanation of the whole of the dif- 

 ierence of the barometric depressions of the summer and winter, so long 

 as we consider the intensities of the whirlwinds proportional to the 

 intensities of the precipitations. 



NOTES. 



No. 1, p. 22. See Zeit. Oest. Gesell.,vol. s, p. 573, The Siroccos of the Southern Alps. 



No. 2, p. 23. For those of our readers to whom this important equation seems strange, 

 and who have neither time nor inclination to look up its demonstration as derived 

 from the fundamental principles of the mechanical theory of heat in the treatises of 

 Clausius or the text-hook of Zeuner, we will endeavor to give in the following as siui- 

 l)le demonstration as possible. 



A mass of air, as is well known, needs a smaller quantity of heat to raise its tem- 

 perature by 1° when we prevent its expansion than when it is allowed to expand. We 

 will denote by c» the quantity of heat which a kilogram of air requires in the first 

 case, that is, when the volume v is constant; and by Cp the quantity required in the 

 second case, when the pressure j9 remains constant, and equal to that of the exterior. 



The dilference between Cp and c^the latter being the greater, arises from the fact 

 that in the case of expansion by heat there is also exterior work performed, which con- 

 sists in the pushing back of the exterior i^ressurep through the small space dv, which 

 is the extent of the expansion. 



The amount of this work is pdr, and the quantity of heat which is thereby con- 

 sumed is —p dv, where — = — — is the equivalent of heat for the unit of work. Con- 

 sequently the quantity of heat dQ which is communicated to the mass of air is 

 divided into two parts ; the one is the equivalent of the increase of temperature of the 

 kilogram of air, the other is the equivalent of the work of expansion, as is expressed 

 in the following equation : 



dQ = Crdt-\-l-pdv. 



u 



The combined law of Mariotte and Gay Lussac reads, as is well known, 



pv p'v' 



l-f ai ■" 1 + at" 



where a = 0.003665 = — — is the coefBcient of expansion of the air. If we divide the 



denominators of both members by a; put T=273H-f, and for the case when <' = 

 pnti? = |2|', V 

 whence follows 



put jB = :^2£?, we obtain the simplest form of this law in the expression pv=^IlT, 



pdv + V d}} = R dt, 

 j)d\}=.Udt — vdp; 



dQ = c,dt + ^ dt- \vdp, 



dQ=(^c.+f\dt-lvdp. 

 According to what has been above said, the difference Cp — c» is equal to the quantity 



